TY - BOOK
AU - Wehrfritz,B.A.F.
ED - SpringerLink (Online service)
TI - Group and Ring Theoretic Properties of Polycyclic Groups
T2 - Algebra and Applications
SN - 9781848829411
AV - QA174-183
U1 - 512.2 23
PY - 2009///
CY - London
PB - Springer London
KW - Mathematics
KW - Associative rings
KW - Rings (Algebra)
KW - Commutative algebra
KW - Commutative rings
KW - Group theory
KW - Group Theory and Generalizations
KW - Associative Rings and Algebras
KW - Commutative Rings and Algebras
N1 - Some Basic Group Theory -- The Basic Theory of Polycyclic Groups -- Some Ring Theory -- Soluble Linear Groups -- Further Group-Theoretic Properties of Polycyclic Groups -- Hypercentral Groups and Rings -- Groups Acting on Finitely Generated Commutative Rings -- Prime Ideals in Polycyclic Group Rings -- The Structure of Modules over Polycyclic Groups -- Semilinear and Skew Linear Groups
N2 - Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations. The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups
UR - http://dx.doi.org/10.1007/978-1-84882-941-1
ER -